A magnetic brake of this type is known from, for instance, U.S. Pat. No. 4,580,742. This known magnetic brake has a plurality of permanent magnets for inductive cooperation with the line spool and a magnet support carrying the magnets. In this known magnetic brake, the braking effect of the brake on the line spool is controlled like in most prior-art magnetic brakes of this kind by the magnet support being displaced in the axial direction of the line spool shaft. This displacement is brought about by turning an adjusting knob. When the braking effect of the brake on the line spool is to be increased, the magnet support is displaced towards the line spool, and when this braking effect is to be reduced, the magnet support is displaced away from the line spool. If a reasonable adjusting range of the braking effect of the magnetic brake on the line spool is to be obtained, the range of displacement of the magnet support must be fairly great, and consequently the magnet support must be given a large space in the fishing reel, at least seen in the axial direction. This requires, in turn, that the fishing reel be given large dimensions. A further drawback is that the magnetic brake exerts a certain braking effect on the line spool even when the magnet support is displaced to its position furthest away from the line spool, i.e. the braking effect cannot be fully canceled.